You are trying to plan for retirement in 10 years, and curently you have $100,00

Question

You are trying to plan for retirement in 10 years, and curently you have $100,000 in a savings account and $300,000 in stocks. In addition you plan on adding to your savings by depositing $10,000 per year in your savings account at the end of

each of the next 5 years and then $20,000 per year at the end of each year for the final 5 years until retirement.

a. Assuming your savings account returns 7 percent compounded annually, and your invest-ment in stocks will return 12 percent compounded annually, how much will you have at the end of 10 years? (Ignore taxes.)

b. If you expect to live for 20 years after you retire, and at retirement you deposit all of your savings in a bank account paying 10 percent, how much can you withdraw each year after retirement (20 equal withdrawals beginning 1 year after you retire) to end up with a zero balance upon your death?

Explanation / Answer

a)
At the end of 10 years,
FV of savings
= 100000*1.07^10 + 10000(1.07^9 +.....!.07^5) + 20000*(1.07^5-1)/0.07
= 196715 + 10000*1.07^5*(1.07^5-1)/0.07 + 20000*(1.07^5-1)/0.07
= 196715 + 80657 + 115015
= 392387 ($)
FV of returns on shares = 300000*1.12^10 = 931754 ($) (rounded off to nearest $)
Total amount at the end of 10 years = 392387 + 931754 = 1324141 ($) (ANSWER)
b)
let a be the amount to be drawn every year.
Then, a*1.1(1.1^20-1)/0.1 = 1324141*1.1^20
= 1324141*1.1^20*0.1/(1.1*(1.1^20-1))
= 141394 ($) (rounded off to nearest $) (ANSWER)   

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